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A000714
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Number of partitions of n, with three kinds of 1 and 2 and two kinds of 3,4,5,....
(Formerly M2777 N1117)
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0
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1, 3, 9, 21, 47, 95, 186, 344, 620, 1078, 1835, 3045, 4967, 7947, 12534, 19470, 29879, 45285, 67924, 100820, 148301, 216199, 312690, 448738, 639464, 905024, 1272837, 1779237, 2473065, 3418655, 4701611, 6434015, 8763676
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 122.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| EULER transform of 3, 3, 2, 2, 2, 2, 2, 2...
G.f.=1/[(1-x)(1-x^2)product((1-x^k)^2, k=1..infinity)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
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EXAMPLE
| a(2)=9 because we have 2, 2', 2", 1+1, 1'+1', 1"+1", 1+1', 1+1", 1'+1".
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MAPLE
| g:=1/((1-x)*(1-x^2)*product((1-x^k)^2, k=1..40)): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..32); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
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MATHEMATICA
| p=Product[1/(1-x^i), {i, 1, 20}]; CoefficientList[Series[p^2/(1 - x)/(1 - x^2), {x, 0, 20}], x] (*Geoffrey Critzer, Nov 28 2011*)
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CROSSREFS
| Sequence in context: A062444 A141156 A014286 * A090984 A006813 A056823
Adjacent sequences: A000711 A000712 A000713 * A000715 A000716 A000717
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Extended with formula from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
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